Abstract

Passive nonlinear absorptive limiters offer an effective means to protect human eyes and other focal-plane sensors from damage by pulsed laser radiation. New device designs are proposed in which dye molecules are driven into strong ground-state depletion by the incoming threat pulse while the internal fluence values are kept below the material failure level. Pulse-energy suppression ratios greater than 104 for 10-ns pulses together with linear transmission greater than 70% should be possible with existing dyes.

© 1994 Optical Society of America

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  1. B. Anderberg, M. L. Wolbarsht, in Laser Weapons, The Dawn of a New Military Age, (Plenum, New York, 1992), Chap. 6, pp. 139–190.
  2. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 4, p. 131.
  3. D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
    [Crossref] [PubMed]
  4. P. A. Miles, “DARPA sensor protection program support,” final rep. under contract F33615-89-C-0532 (Logicon RDA, Los Angeles, Calif., 1991).
  5. R. C. Hoffman, K. A. Stetyick, R. S. Potember, D. G. McLean, “Reverse saturable absorbers: indanthrone and its derivatives,” J. Opt. Soc. Am. B 6, 772–777 (1989).
    [Crossref]
  6. D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).
  7. L. W. Tutt, S. W. McCahon, “Reverse saturable absorption in metal cluster compounds,” Opt. Lett. 15, 700–702 (1990).
    [Crossref] [PubMed]
  8. S. W. McCahon, L. W. Tutt, M. B. Klein, G. C. Valley, “Optical limiting with reverse saturable absorbers,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.,1307, 304–314 (1990).
  9. L. W. Tutt, S. W. McCahon, M. B. Klein, “Optimization of optical limiting properties of organometallic compound,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo. Opt. Instrum. Eng.1307, 315–326 (1990).
  10. L. W. Tutt, S. W. McCahon, M. B. Klein, “Nonlinear optical properties of organometallic compounds in solids and solutions,” in Nonlinear Optics: Materials, Phenomena, and Devices (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 57–58.
    [Crossref]
  11. J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).
  12. L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.
  13. T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
    [Crossref]
  14. K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).
  15. P. A. Miles, “Transient photochromic limiters for eye protection,” Logicon RDA white paper (Logicon RDA, Los Angeles, Calif., 1991).
  16. S. W. McCahon, L. W. Tutt, “Optical limiter including optical convergence and absorbing body with inhomogeneous distribution of reverse saturable material,” U.S. patent5,080,469 (14January1992).
  17. T. J. Gleason, J. L. Scales, “System considerations for advanced eye and sensor protection,” draft Rep.U.S. Army LABCOM, Adelphi, Md., 1991).
  18. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 7, pp. 218–219.
  19. B. Anderberg, M. Wolbarsht, Laser Weapons, The Dawn of a New Military Age (Plenum, New York, 1992), Chap. 3, pp. 78–79.
  20. N. G. Wagner, B. A Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
    [Crossref]
  21. H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
    [Crossref]
  22. J. J. Zayhowski, P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron. 27, 2220–2225 (1991).
    [Crossref]
  23. C. R. Giuliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).”
    [Crossref]
  24. D. J. Harter, M. L. Shand, Y. B. Band, “Power/energy limiter using reverse saturable absorption,” J. Appl. Phys. 56, 865–868 (1984).
    [Crossref]
  25. L. W. Tutt, A. Kost, “Optical limiting performance of C60 and C70 solutions,” Nature (London) 356, 225–226 (1992).
    [Crossref]
  26. A. Kost, L. W. Tutt, M. B. Klein, “Optical limiting with C60 in polymethyl methacrylate,” Opt. Lett. 18, 334–336 (1993).
    [Crossref] [PubMed]
  27. I. Carmichael, G. L. Hug, “Triplet–triplet absorption spectra of organic molecules in condensed phases,” J. Phys. Chem. Ref. Data 15, 1–250 (1986).
    [Crossref]
  28. K. Mansour, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. 91109 (personal communication, October1993).
  29. P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, 801–818 (1965).
    [Crossref]
  30. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
    [Crossref]
  31. V. V. Arsen’ev, D. N. Klyshko Dneprovskii, A. N. Penin, “Nonlinear absorption and limitation of light intensity in semiconductors,” Sov. Phys. JETP 29, 413–415 (1969).
  32. J. M. Ralston, R. K. Chang, “Optical limitingin semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
    [Crossref]
  33. Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).
  34. T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
    [Crossref]
  35. M. Born, E. Wolf, “The three dimensional light distribution near focus,” Principles of Optics (Pergamon, New York, 1959), pp. 434–448.

1993 (1)

1992 (2)

L. W. Tutt, A. Kost, “Optical limiting performance of C60 and C70 solutions,” Nature (London) 356, 225–226 (1992).
[Crossref]

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

1991 (3)

J. J. Zayhowski, P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron. 27, 2220–2225 (1991).
[Crossref]

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

1990 (1)

1989 (2)

D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
[Crossref] [PubMed]

R. C. Hoffman, K. A. Stetyick, R. S. Potember, D. G. McLean, “Reverse saturable absorbers: indanthrone and its derivatives,” J. Opt. Soc. Am. B 6, 772–777 (1989).
[Crossref]

1986 (1)

I. Carmichael, G. L. Hug, “Triplet–triplet absorption spectra of organic molecules in condensed phases,” J. Phys. Chem. Ref. Data 15, 1–250 (1986).
[Crossref]

1985 (1)

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

1984 (1)

D. J. Harter, M. L. Shand, Y. B. Band, “Power/energy limiter using reverse saturable absorption,” J. Appl. Phys. 56, 865–868 (1984).
[Crossref]

1983 (1)

Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).

1975 (1)

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
[Crossref]

1969 (2)

V. V. Arsen’ev, D. N. Klyshko Dneprovskii, A. N. Penin, “Nonlinear absorption and limitation of light intensity in semiconductors,” Sov. Phys. JETP 29, 413–415 (1969).

J. M. Ralston, R. K. Chang, “Optical limitingin semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[Crossref]

1967 (1)

C. R. Giuliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).”
[Crossref]

1965 (1)

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, 801–818 (1965).
[Crossref]

1963 (1)

N. G. Wagner, B. A Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[Crossref]

Abodie, B.

D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
[Crossref] [PubMed]

Allan, G. R.

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Alvarez, D.

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

Anderberg, B.

B. Anderberg, M. Wolbarsht, Laser Weapons, The Dawn of a New Military Age (Plenum, New York, 1992), Chap. 3, pp. 78–79.

B. Anderberg, M. L. Wolbarsht, in Laser Weapons, The Dawn of a New Military Age, (Plenum, New York, 1992), Chap. 6, pp. 139–190.

Arsen’ev, V. V.

V. V. Arsen’ev, D. N. Klyshko Dneprovskii, A. N. Penin, “Nonlinear absorption and limitation of light intensity in semiconductors,” Sov. Phys. JETP 29, 413–415 (1969).

Band, Y. B.

D. J. Harter, M. L. Shand, Y. B. Band, “Power/energy limiter using reverse saturable absorption,” J. Appl. Phys. 56, 865–868 (1984).
[Crossref]

Boggess, T. F.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Born, M.

M. Born, E. Wolf, “The three dimensional light distribution near focus,” Principles of Optics (Pergamon, New York, 1959), pp. 434–448.

Boyd, I. W.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

Brouvillet, B.

D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
[Crossref] [PubMed]

Carmichael, I.

I. Carmichael, G. L. Hug, “Triplet–triplet absorption spectra of organic molecules in condensed phases,” J. Phys. Chem. Ref. Data 15, 1–250 (1986).
[Crossref]

Chang, R. K.

J. M. Ralston, R. K. Chang, “Optical limitingin semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[Crossref]

Choong, I.

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

Coulter, D. R.

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

Courant, D.

D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
[Crossref] [PubMed]

Court, L.

D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
[Crossref] [PubMed]

Danilelko, Y. K.

Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).

Giuliano, C. R.

C. R. Giuliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).”
[Crossref]

Gleason, T. J.

T. J. Gleason, J. L. Scales, “System considerations for advanced eye and sensor protection,” draft Rep.U.S. Army LABCOM, Adelphi, Md., 1991).

Hagan, D. J.

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

Harter, D. J.

D. J. Harter, M. L. Shand, Y. B. Band, “Power/energy limiter using reverse saturable absorption,” J. Appl. Phys. 56, 865–868 (1984).
[Crossref]

Haus, H. A.

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
[Crossref]

Hess, L. D.

C. R. Giuliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).”
[Crossref]

Hoffman, R. C.

Hogan, D. J.

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Hug, G. L.

I. Carmichael, G. L. Hug, “Triplet–triplet absorption spectra of organic molecules in condensed phases,” J. Phys. Chem. Ref. Data 15, 1–250 (1986).
[Crossref]

Kelley, P. L.

J. J. Zayhowski, P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron. 27, 2220–2225 (1991).
[Crossref]

Khundkar, L. R.

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

Klein, M. B.

A. Kost, L. W. Tutt, M. B. Klein, “Optical limiting with C60 in polymethyl methacrylate,” Opt. Lett. 18, 334–336 (1993).
[Crossref] [PubMed]

L. W. Tutt, S. W. McCahon, M. B. Klein, “Nonlinear optical properties of organometallic compounds in solids and solutions,” in Nonlinear Optics: Materials, Phenomena, and Devices (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 57–58.
[Crossref]

L. W. Tutt, S. W. McCahon, M. B. Klein, “Optimization of optical limiting properties of organometallic compound,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo. Opt. Instrum. Eng.1307, 315–326 (1990).

S. W. McCahon, L. W. Tutt, M. B. Klein, G. C. Valley, “Optical limiting with reverse saturable absorbers,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.,1307, 304–314 (1990).

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Klyshko Dneprovskii, D. N.

V. V. Arsen’ev, D. N. Klyshko Dneprovskii, A. N. Penin, “Nonlinear absorption and limitation of light intensity in semiconductors,” Sov. Phys. JETP 29, 413–415 (1969).

Kost, A.

A. Kost, L. W. Tutt, M. B. Klein, “Optical limiting with C60 in polymethyl methacrylate,” Opt. Lett. 18, 334–336 (1993).
[Crossref] [PubMed]

L. W. Tutt, A. Kost, “Optical limiting performance of C60 and C70 solutions,” Nature (London) 356, 225–226 (1992).
[Crossref]

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Labergeries, D. R.

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Lebedeva, T. P.

Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).

Lengyel, B. A

N. G. Wagner, B. A Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[Crossref]

Maker, P. D.

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, 801–818 (1965).
[Crossref]

Mansour, K.

K. Mansour, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. 91109 (personal communication, October1993).

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

Marder, S. R.

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

McCahon, S. W.

L. W. Tutt, S. W. McCahon, “Reverse saturable absorption in metal cluster compounds,” Opt. Lett. 15, 700–702 (1990).
[Crossref] [PubMed]

S. W. McCahon, L. W. Tutt, M. B. Klein, G. C. Valley, “Optical limiting with reverse saturable absorbers,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.,1307, 304–314 (1990).

L. W. Tutt, S. W. McCahon, M. B. Klein, “Optimization of optical limiting properties of organometallic compound,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo. Opt. Instrum. Eng.1307, 315–326 (1990).

L. W. Tutt, S. W. McCahon, M. B. Klein, “Nonlinear optical properties of organometallic compounds in solids and solutions,” in Nonlinear Optics: Materials, Phenomena, and Devices (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 57–58.
[Crossref]

S. W. McCahon, L. W. Tutt, “Optical limiter including optical convergence and absorbing body with inhomogeneous distribution of reverse saturable material,” U.S. patent5,080,469 (14January1992).

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

McLean, D. G.

Miles, P. A.

P. A. Miles, “DARPA sensor protection program support,” final rep. under contract F33615-89-C-0532 (Logicon RDA, Los Angeles, Calif., 1991).

P. A. Miles, “Transient photochromic limiters for eye protection,” Logicon RDA white paper (Logicon RDA, Los Angeles, Calif., 1991).

Miskowski, V. M.

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

Moss, S. C.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

Penin, A. N.

V. V. Arsen’ev, D. N. Klyshko Dneprovskii, A. N. Penin, “Nonlinear absorption and limitation of light intensity in semiconductors,” Sov. Phys. JETP 29, 413–415 (1969).

Perry, J. W.

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

Perry, K. J.

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

Potember, R. S.

Prokhorov, A. M.

Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).

Ralston, J. M.

J. M. Ralston, R. K. Chang, “Optical limitingin semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[Crossref]

Rychnovsky, S. R.

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

Scales, J. L.

T. J. Gleason, J. L. Scales, “System considerations for advanced eye and sensor protection,” draft Rep.U.S. Army LABCOM, Adelphi, Md., 1991).

Sence, M. J.

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

Shand, M. L.

D. J. Harter, M. L. Shand, Y. B. Band, “Power/energy limiter using reverse saturable absorption,” J. Appl. Phys. 56, 865–868 (1984).
[Crossref]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

Sidorin, A. V.

Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 7, pp. 218–219.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 4, p. 131.

Smirl, A. L.

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

Stetyick, K. A.

Terhune, R. W.

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, 801–818 (1965).
[Crossref]

Tutt, L. W.

A. Kost, L. W. Tutt, M. B. Klein, “Optical limiting with C60 in polymethyl methacrylate,” Opt. Lett. 18, 334–336 (1993).
[Crossref] [PubMed]

L. W. Tutt, A. Kost, “Optical limiting performance of C60 and C70 solutions,” Nature (London) 356, 225–226 (1992).
[Crossref]

L. W. Tutt, S. W. McCahon, “Reverse saturable absorption in metal cluster compounds,” Opt. Lett. 15, 700–702 (1990).
[Crossref] [PubMed]

S. W. McCahon, L. W. Tutt, M. B. Klein, G. C. Valley, “Optical limiting with reverse saturable absorbers,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.,1307, 304–314 (1990).

L. W. Tutt, S. W. McCahon, M. B. Klein, “Optimization of optical limiting properties of organometallic compound,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo. Opt. Instrum. Eng.1307, 315–326 (1990).

L. W. Tutt, S. W. McCahon, M. B. Klein, “Nonlinear optical properties of organometallic compounds in solids and solutions,” in Nonlinear Optics: Materials, Phenomena, and Devices (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 57–58.
[Crossref]

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

S. W. McCahon, L. W. Tutt, “Optical limiter including optical convergence and absorbing body with inhomogeneous distribution of reverse saturable material,” U.S. patent5,080,469 (14January1992).

Valley, G. C.

S. W. McCahon, L. W. Tutt, M. B. Klein, G. C. Valley, “Optical limiting with reverse saturable absorbers,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.,1307, 304–314 (1990).

Van Stryland, E. W.

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

Wagner, N. G.

N. G. Wagner, B. A Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[Crossref]

Wei, T. H.

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 4, p. 131.

B. Anderberg, M. Wolbarsht, Laser Weapons, The Dawn of a New Military Age (Plenum, New York, 1992), Chap. 3, pp. 78–79.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 7, pp. 218–219.

Wolbarsht, M. L.

B. Anderberg, M. L. Wolbarsht, in Laser Weapons, The Dawn of a New Military Age, (Plenum, New York, 1992), Chap. 6, pp. 139–190.

Wolf, E.

M. Born, E. Wolf, “The three dimensional light distribution near focus,” Principles of Optics (Pergamon, New York, 1959), pp. 434–448.

Zayhowski, J. J.

J. J. Zayhowski, P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron. 27, 2220–2225 (1991).
[Crossref]

Appl. Phys. B (1)

T. H. Wei, D. J. Hogan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurement of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Appl. Phys. Lett. (1)

J. M. Ralston, R. K. Chang, “Optical limitingin semiconductors,” Appl. Phys. Lett. 15, 164–166 (1969).
[Crossref]

Health Phys. (1)

D. Courant, L. Court, B. Abodie, B. Brouvillet, “Retinal damage thresholds from single-pulse laser exposures in the visible spectrum,” Health Phys. 56, 637–642 (1989).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (3)

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. QE-11, 736–746 (1975).
[Crossref]

J. J. Zayhowski, P. L. Kelley, “Optimization of Q-switched lasers,” IEEE J. Quantum Electron. 27, 2220–2225 (1991).
[Crossref]

C. R. Giuliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).”
[Crossref]

J. Appl. Phys. (2)

D. J. Harter, M. L. Shand, Y. B. Band, “Power/energy limiter using reverse saturable absorption,” J. Appl. Phys. 56, 865–868 (1984).
[Crossref]

N. G. Wagner, B. A Lengyel, “Evolution of the giant pulse in a laser,” J. Appl. Phys. 34, 2040–2046 (1963).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. Ref. Data (1)

I. Carmichael, G. L. Hug, “Triplet–triplet absorption spectra of organic molecules in condensed phases,” J. Phys. Chem. Ref. Data 15, 1–250 (1986).
[Crossref]

J. Quantum Electron. (1)

T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, “Optical limiting in GaAs,” J. Quantum Electron. QE-21, 488–494 (1985).
[Crossref]

NATO Adv. Stud. Ser. E (1)

J. W. Perry, L. R. Khundkar, D. R. Coulter, D. Alvarez, S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, D. J. Hagan, “Organic molecules for nonlinear optics and photonics,” NATO Adv. Stud. Ser. E 194, 369–382 (1991).

Nature (London) (1)

L. W. Tutt, A. Kost, “Optical limiting performance of C60 and C70 solutions,” Nature (London) 356, 225–226 (1992).
[Crossref]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 1228–1235 (1991).
[Crossref]

Opt. Lett. (2)

Phys. Rev. (1)

P. D. Maker, R. W. Terhune, “Study of optical effects due to an induced polarization third order in the electric field strength,” Phys. Rev. 137, 801–818 (1965).
[Crossref]

Sov. Phys. JETP (2)

V. V. Arsen’ev, D. N. Klyshko Dneprovskii, A. N. Penin, “Nonlinear absorption and limitation of light intensity in semiconductors,” Sov. Phys. JETP 29, 413–415 (1969).

Y. K. Danilelko, T. P. Lebedeva, A. M. Prokhorov, A. V. Sidorin, “Dynamics of nonlinear absorption of light in solids,” Sov. Phys. JETP 57, 1183–1187 (1983).

Other (16)

M. Born, E. Wolf, “The three dimensional light distribution near focus,” Principles of Optics (Pergamon, New York, 1959), pp. 434–448.

K. Mansour, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif. 91109 (personal communication, October1993).

S. W. McCahon, L. W. Tutt, M. B. Klein, G. C. Valley, “Optical limiting with reverse saturable absorbers,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo-Opt. Instrum. Eng.,1307, 304–314 (1990).

L. W. Tutt, S. W. McCahon, M. B. Klein, “Optimization of optical limiting properties of organometallic compound,” in Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors, R. Hartmann, M. J. Soileau, V. K. Varadan, eds., Proc. Soc. Photo. Opt. Instrum. Eng.1307, 315–326 (1990).

L. W. Tutt, S. W. McCahon, M. B. Klein, “Nonlinear optical properties of organometallic compounds in solids and solutions,” in Nonlinear Optics: Materials, Phenomena, and Devices (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 57–58.
[Crossref]

P. A. Miles, “DARPA sensor protection program support,” final rep. under contract F33615-89-C-0532 (Logicon RDA, Los Angeles, Calif., 1991).

B. Anderberg, M. L. Wolbarsht, in Laser Weapons, The Dawn of a New Military Age, (Plenum, New York, 1992), Chap. 6, pp. 139–190.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 4, p. 131.

L. W. Tutt, S. W. McCahon, A. Kost, M. B. Klein, T. F. Boggess, G. R. Allan, S. R. Rychnovsky, D. R. Labergeries, A. L. Smirl, “Organometallics for optical limiting devices,” in Proceedings of the First International Conference on Intelligent Materials, T. Tagaki, ed. (Technomic, Lancaster, Pa., 1993), pp. 165–174.

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines and naphthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1105, 42–51 (1989).

K. Mansour, D. Alvarez, K. J. Perry, I. Choong, S. R. Marder, J. W. Perry, “Dynamics of optical limiting in heavy-atom substituted phthalocyanines,” in Organic and Biological Optoelectronics, P. M. Rentzepis, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1853, 132–141 (1993).

P. A. Miles, “Transient photochromic limiters for eye protection,” Logicon RDA white paper (Logicon RDA, Los Angeles, Calif., 1991).

S. W. McCahon, L. W. Tutt, “Optical limiter including optical convergence and absorbing body with inhomogeneous distribution of reverse saturable material,” U.S. patent5,080,469 (14January1992).

T. J. Gleason, J. L. Scales, “System considerations for advanced eye and sensor protection,” draft Rep.U.S. Army LABCOM, Adelphi, Md., 1991).

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sensors (Plenum, New York, 1980), Chap. 7, pp. 218–219.

B. Anderberg, M. Wolbarsht, Laser Weapons, The Dawn of a New Military Age (Plenum, New York, 1992), Chap. 3, pp. 78–79.

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Figures (18)

Fig. 1
Fig. 1

Total pulse energy entering the eye at visual wavelengths for a 50% probability of retinal lesion formation (Ref. 18).

Fig. 2
Fig. 2

Temporal irradiance and fluence profiles for a symmetrical secant hyperbolic pulse.

Fig. 3
Fig. 3

Energy-versus-characteristic-time profile for secant hyperbolic (solid curve) and flat-top (dashed lines) pulsed threats in relation to eye-safe levels at visual wavelengths.

Fig. 4
Fig. 4

Simplified seven-level model relevant to the response of organic dye molecules to optical radiation.

Fig. 5
Fig. 5

Normalized ground-state singlet–singlet and excited-state triplet–triplet absorption spectra for the metallo-organic SnPc in toluene (Ref. 28).

Fig. 6
Fig. 6

Characteristic fluence dependence of the molecular absorption coefficient, plotted for σeg = 30, Fs = hν/Φσg.

Fig. 7
Fig. 7

Geometry of beam focused at the exit plane of a nonlinear absorptive element.

Fig. 8
Fig. 8

Longitudinal fluence profile for a beam focused at the exit face of a quadratic nonlinear absorber and its dependence on input energy E0. The plot is normalized to the exit fluence F at transmitted energy limit E.

Fig. 9
Fig. 9

Relationships among minimum possible f/#’s for quadratic limiters, transmitted energy, nonlinear absorption constant, and focal-plane heating limits when the focal plane lies within the nonlinear material. Point A, transmitted energy limit 1 μJ; point B, f/5 optical system.

Fig. 10
Fig. 10

Spherically convergent light beam passing through a nonlinear element. The typical bottleneck limiter configuration places the beam waist beyond the exit face.

Fig. 11
Fig. 11

Computed input–output energy characteristic for abottleneck limiter with a linear transmittance of 0.8 and a maximum suppression ratio of 808. Energies are scaled to the transmitted energy for an exit fluence F(ze) = Fs = hν/Φσg. The shape of a hypothetical quadratic limiter designed to hard limit at the same output energy is shown for comparison.

Fig. 12
Fig. 12

Maximum allowable fluence, Fmax, based on nonlinear absorption as a function of concentration of dye molecules, N0 (solid curve). The curve for the specific case of σeg = 30 and for Fmatrix = 25 Fs is drawn. Normalized values of Nmax and Ncrit determined from the fully saturated absorption asymptote are also indicated.

Fig. 13
Fig. 13

Molecular concentration profiles needed to maintain constant fluence, independent of axial position, in saturated bottleneck limiters.

Fig. 14
Fig. 14

Molecular concentration profile needed to maintain specific levels of either volumetric heating or fluence in a SnPc bottleneck limiter. The associated energy profile (dashed curve) is based on the assumption of an f/5 optics. The exit plane is 116 μm from the ray convergence point.

Fig. 15
Fig. 15

Molecular concentration profile appropriate for a SnPc bottleneck limiter—uniform cap design. The associated energy profile (dashed curve) is based on the assumption of an f/5 optics.

Fig. 16
Fig. 16

Calculated fluence profiles for bottleneck f/5 optical limiter designs in SnPc: (a) z−1 molecular concentration profile, (b) uniform concentration cap, (c) extension to focal plane.

Fig. 17
Fig. 17

Molecular concentration and energy profiles for a SnPc bottleneck f/5 optical limiter—cap extension to focal plane with transmitted energy ET = 4.4 × 10−8 J.

Fig. 18
Fig. 18

Four-plate SnPc bottleneck f/5 limiter, index matched at n = 1.5, for E0 = 27 mJ, ET = 2.0 μJ. (Total nonlinear material thickness 1.42 mm.)

Tables (2)

Tables Icon

Table 1 Time Constants, Triplet Yields and Absorption Cross Sections at λ0 = 532 nm for Various Dye Molecules in Solution (Ref. 14)

Tables Icon

Table 2 Design Characteristics of a Four-Plate Limiter Using SnPc

Equations (64)

Equations on this page are rendered with MathJax. Learn more.

I ( t ) = I 0 sech 2 t τ ,             F ( t ) = 0.5 F 0 ( 1 + tanh t τ ) ,
n g = N 0 exp ( - F / F s ) ,             F s = h ν / Φ σ g ,
n s / n t = τ / τ s t ,
σ m ( F ) = σ g exp ( - F / F s ) + σ e [ 1 - exp ( - F / F s ) ] .
σ m σ g ( 1 + γ F ) ,             F F s γ = Φ ( σ e - σ g ) / h ν .
- d I d z = ( α 0 + β I ) I ,
- d I d z = α 0 ( 1 + γ F ) ,             F ( t ) = - t I ( t ) d t .
D ( z ) = ( κ 2 z 2 + w 0 2 ) 1 / 2 ,             κ - 1 = n f / # .
E ( z ) = E 0 exp [ - α 0 ( z + L ) ] , I ( z ) = I 0 exp [ - α 0 ( z + L ) ] ( κ 2 L 2 + w 0 2 ) ( κ 2 z 2 + w 0 2 ) - 1 .
E ( z , t ) = E 0 ( t ) exp [ - α 0 ( z + L ) ] [ 1 + γ α 0 E 0 ( t ) Ω * ] - 1 ,
Ω * = 2 π - L z exp [ - α 0 ( x + L ) ] κ 2 x 2 + w 0 2 d x .
E = ɛ λ 0 n ( γ α 0 ) - 1 ,
( f / # ) min = ( π 2 8 n ɛ 3 λ 0 3 C v Δ T m ) 1 / 4 E 1 / 4 .
E max = π 4 κ 2 L 2 F max = π 4 κ 2 L 2 ( 2 C v Δ T m γ α 0 ) 1 / 2 .
S = π n 4 ɛ λ 0 ( 2 C v Δ T m γ α 0 ) 1 / 2 κ 2 L 2
S m = π 2 8 C v Δ T m γ α 0 L 2 .
γ α 0 = N 0 σ g Φ ( σ e - σ g ) / h ν ,
σ e σ g | F S 8 C v Δ T m Φ h ν 1 N 0 , σ e σ g | S , T 8 π 2 S ln 2 T h ν Φ C v Δ T m N 0 .
( σ e σ g ) min = σ ¯ e σ ¯ g = 8 π ( S 1 / 2 - ln T ) ,
N ¯ 0 = π Φ C v Δ T m h ν ( - ln T S 1 / 2 ) .
σ ¯ g = h ν Φ ( λ 0 8 n C v Δ T m E ) 1 / 2 5.3 × 10 - 19 cm 2 , σ ¯ e = 3.8 × 10 - 16 cm 2 .
E T = E 0 exp [ - σ g N 0 ( z ) d z ]
E T = E 0 exp [ - σ e N 0 ( z ) d z ] .
ln S m - ln T = σ e σ g .
Δ H = 0 F α ( f ) d f = N 0 σ H F ,
σ H = σ e - ( σ e - σ g ) F s F [ 1 - exp ( - F F s ) ] .
F max F s = ( 1 - σ g σ e ) [ 1 - exp ( - F max F s ) ] + C v Δ T m σ e F s 1 N 0 ,
N 0 σ e F max = C v Δ T m , N 0 σ g F max = C v Δ T m ,
N max = C v Δ T m 2.5 F s σ H .
N 0 ( z ) σ H ( z ) = C v Δ T m / F max ( z )
N 0 ( z ) σ m ( z ) = - 1 E ( z ) d E ( z ) d z ,
1 E ( z ) d E ( z ) d z 1 D 2 ( z ) d D 2 ( z ) d z .
N ( z ) = 2 κ 2 z σ m - 1 κ 2 z 2 + w 0 2 2 σ m z ,             κ z w 0 .
N ( z ) = N M y y 2 + a 2 ,
N M = 2 σ m λ 0 ,             y = z λ 0 ,             a = n ( f / # ) 2 .
- d E ( z ) d z = π 4 Δ H D 2 ( z ) = π 4 Δ H ( κ 2 z 2 + w 0 2 ) .
E - E e = π 4 Δ H ( 1 3 κ 2 z 3 + w 0 2 z ) .
4 π E ( z ) Δ H = 1 3 κ 2 ( z e 3 - z 3 ) + w 0 2 ( z e - z ) + F ( z e ) Δ H ( κ 2 z e 2 + w 0 2 ) ,             z > z e .
F max ( z ) Δ H = [ 1 3 κ 2 ( z e 3 - z 3 ) + w 0 2 ( z e - z ) + z H ( κ 2 z e 2 + w 0 2 ) ] × [ κ 2 z 2 + w 0 2 ] - 1 ,
z H = F ( z e ) Δ H .
N 0 ( z ) = Δ H σ e F max - 1 ( z ) .
E ( z ) = π 4 κ 2 z e 2 F ( z e ) + π 4 Δ H 3 κ 2 ( z e 3 - z 3 )             z > z e = π Δ H κ 2 z e 3 12 [ 1 - ( z z e ) 3 + 3 z H z e ] .
E ( z ) = - π κ 2 Δ H 12 z 3 , or E E T = z 3 z e 3 .
E T = π 12 ( κ C v Δ T m ) 2 ( 7.5 F s ) 3 = 110.4 ( κ C v Δ T m ) 2 ( h ν Φ σ g ) 3 .
d E d z = π Δ H 4 κ 2 z 2 ,
N 0 ( z ) σ H ( z ) = 1 E d E d z = 3 z .
N 0 = N max z e z             z > z e ,
N max = 3 σ e z e = C v Δ T m 2.5 F s σ e = C v Δ T m 2.5 σ e Φ σ g h ν .
F ( z ) = - π κ 2 Δ H 12 z 3 ( π / 4 ) κ 2 z 2 = - Δ H 3 z .
z < z crit = 3 F matrix C v Δ T m .
exp [ - N 0 σ e ( 3 z H - z e ) ] = ( z e 3 z H ) 2 or exp [ - 3 ( 1 - x ) ] = x 2 ,             x = z e 3 z H .
z e = 0.417 ( 3 z H ) .
z e = 48.4 μ m ,             E T = 0.30 μ J .
E T = π 4 w 0 2 F ( 0 ) ,
E ( z ) = E T - π 4 Δ H ( 1 3 κ 2 z 3 + w 0 2 z ) ,
F ( z ) = [ w 0 2 F ( 0 ) - Δ H ( 1 3 κ 2 z 3 + w 0 2 z ) ] × ( κ 2 z 2 + w 0 2 ) - 1 = F ( 0 ) [ a 2 + ω y ( y 2 + 3 a 2 ) ] ( y 2 + a 2 ) - 1 ,
y = z λ 0 ,             ω = Δ H λ 0 3 F ( 0 ) ,             a = ɛ n ( f / # ) 2 .
N 0 ( z ) = Δ H F ( z ) σ H ( z ) = Δ H F ( 0 ) σ H ( y 2 + a 2 ) [ a 2 + ω y ( y 2 + 3 a 2 ) ] - 1 = 3 σ H λ 0 ( y 2 + a 2 ) [ a 2 ω - 1 + y ( y 2 + 3 a 2 ) ] - 1 .
N 0 ( z ) = 3 σ e λ 0 ( y 2 + a 2 ) [ a 2 ω - 1 + y ( y 2 + 3 a 2 ) ] - 1 , ω = C v Δ T m λ 0 Φ σ g 7.5 h ν .
N ( z ) = N 0 [ 1 + ( y a ) x ] - 1 ,             x ~ 1.5 ,
exp ( + N 0 σ e l i ) = ρ ( z i + l i ) 2 z i 2 ,
exp ( g i x ) = ρ ( 1 + x ) 2 ,
z m = 2 / N 0 σ e .
e - y ¯ = ρ ( 1 - y ¯ ) ,             y ¯ = l + / z m .

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